Math Problem Statement

a) What is µ, and ox (sigma chi), for this distribution? Round values to two decimal places if needed.

What is µ (mean) and σ (standard deviation) for this distribution? Round values to two decimal places if needed.

Solution

Based on the images provided, here is the information about the normal distribution:

  • μ (mean) = 119.7
  • σ (standard deviation) = 10.9

These values describe the normal distribution where the probability P(99.7X143.1)P(99.7 \leq X \leq 143.1) is approximately 0.9508.

Would you like more details or have any specific questions?

Here are 5 related questions to deepen your understanding:

  1. What does the value of μ\mu represent in the context of a normal distribution?
  2. How does the standard deviation σ\sigma affect the shape of a normal distribution?
  3. What percentage of the data lies within 1 standard deviation of the mean in this normal distribution?
  4. How would you interpret the probability P(99.7X143.1)=0.9508P(99.7 \leq X \leq 143.1) = 0.9508?
  5. How does changing μ\mu and σ\sigma affect the probabilities in a normal distribution?

Tip: In a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, and 95% within two standard deviations.

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Math Problem Analysis

Mathematical Concepts

Normal Distribution
Probability

Formulas

P(a ≤ X ≤ b) = 0.9508
Standard Normal Formula Z = (X - µ) / σ

Theorems

Empirical Rule

Suitable Grade Level

Grades 10-12